### Disappointment Aversion function library
## Appendix Theory: A.4.3


MaxLikeSR_disapAver_LOO_crossVal = function(data, sub_sample, init, elation=FALSE){
  # Leave-one-out Cross Validation (LOO CV)
  # elation=True removes the lower bound on beta (removes beta>=0) by changing the wrapMLE_ function
  start <- Sys.time()  
  data = sample_SR(data,sub_sample)
  index = data$studentID                                                            
  data = split(data,f = index)  
  
  dfs_LOOCV = lapply(data, LOOCV_train_test_split)
  results = lapply(dfs_LOOCV, LOO_crossVal_train_predict_disapAver, init, elation)
  beta_coef = unlist(lapply(results, {function(x) mean(x[["beta.coef"]])}), use.names = FALSE)
  beta_coef_std = unlist(lapply(results, {function(x) sqrt(var(x[["beta.coef"]]))}), use.names = FALSE)
  score = unlist(lapply(results, {function(x) sum(x$accuracy)}), use.names = FALSE)
  results_scores = as.data.frame(cbind(studentID = unique(index), score = score, beta_mean = beta_coef, beta_std = beta_coef_std))
  
  print("Dissapointment Aversion - Leave-One-Out Test Accuracy Summary:")
  print(paste("Average:", mean(results_scores$score)))
  print(paste("Standard error:", sqrt(var(results_scores$score)/length(results_scores$score))))
  
  end = Sys.time()                                                                  
  timer = difftime(end,start,units = "secs")
  print(paste("Time taken for MLE algorithim and Cross-Validation:",seconds_to_period(round(timer[[1]],2))))
  return(list(estimations = results, summary = results_scores))
}



LOOCV_train_test_split = function(data){
  result = list()
  for(i in 1:length(data$qnum)){
    test_df = data[i, ]
    train_df = data[-i, ]
    result[[i]] <- list(train = train_df, test = test_df)
  }
  result
}



LOO_crossVal_train_predict_disapAver = function(LOO_train_test_folds, init, elation){
  results = bind_rows(lapply(LOO_train_test_folds, LOO_train_test_disapAver, init, elation))
  results
}



LOO_train_test_disapAver = function(train_test_dfs, init, elation){
  train_df = train_test_dfs[["train"]]
  test_df = train_test_dfs[["test"]]
  
  if(elation==TRUE){results = wrapMLE_disappointment_elation(train_df, init, log_lik_disapAver)}
  else{results = wrapMLE_disappointment(train_df, init, log_lik_disapAver)}
  results_summary = stat_sum_disapAver(results)
  results_summary$studentID = test_df$studentID
  
  param = list(beta = results_summary$beta.coef)
  test_predict_results = LOO_test_predict(test_df, param, calc_util_disapAver)
  results_summary = cbind(results_summary, test_qnum = test_df$qnum, test_choice = test_df$choice, test_predict_results)
  results_summary
}





LOO_test_predict = function(test_df, param, util_fun){
  lottery_data = list(l1 = list(prob = test_df[["prob.1"]], lower = test_df[["lower.1"]], upper = test_df[["upper.1"]]),
                      l2 = list(prob = test_df[["prob.2"]], lower = test_df[["lower.2"]], upper = test_df[["upper.2"]]),
                      l3 = list(prob = test_df[["prob.3"]], lower = test_df[["lower.3"]], upper = test_df[["upper.3"]]),
                      l4 = list(prob = test_df[["prob.4"]], lower = test_df[["lower.4"]], upper = test_df[["upper.4"]]),
                      l5 = list(prob = test_df[["prob.5"]], lower = test_df[["lower.5"]], upper = test_df[["upper.5"]]))
  
  lottery_utility = unlist(lapply(lottery_data, util_fun, param))
  predicted_choice = unname(which.max(lottery_utility))
  accuracy = if_else(predicted_choice == test_df$choice, 1, 0)
  list(pred_choice = predicted_choice, accuracy = accuracy)
}



calc_util_disapAver = function(df, param){
  w_pH(param[["beta"]],df[["prob"]])*df[["upper"]] + w_pL(param[["beta"]],df[["prob"]])*df[["lower"]]
}


w_pH <- function(param, prob){
  (1-(((1-prob)*param)/(1+(1-prob)*param)))*prob
}

w_pL <- function(param, prob){
  (1+((prob*param)/(1+(1-prob)*param)))*(1-prob)
} 


wrapMLE_disappointment = function(data,init,logLikFun){
  disapAver_MaxLike_res = mle2(minuslogl = logLikFun, data = list(data=data), start = init,
                             method="L-BFGS-B", optimizer = "optim", lower = c(beta=0))
  disapAver_MaxLike_res
}


wrapMLE_disappointment_elation = function(data,init,logLikFun){
  disapAver_MaxLike_res = mle2(minuslogl = logLikFun, data = list(data=data), start = init)
  disapAver_MaxLike_res
}


stat_sum_disapAver = function(stat){
  results = data.frame("studentID"=NA,"beta.coef"=NA,
                       "std.beta"=NA,"p.val.beta"=NA,
                       "logLikelihood"=NA,"AIC"=NA)
  summary = summary(stat)
  results["studentID"]  = NA
  results["beta.coef"]  = summary@coef[1,1]
  results["std.beta"]   = summary@coef[1,2]
  results["p.val.beta"] = summary@coef[1,4]
  results["logLikelihood"] = logLik(stat)
  results["AIC"]  = AIC(stat)
  return(results)
}



log_lik_disapAver <- function(beta, data){
  
  #calculating denominator of likelihood of a choice
  denomCalc = function(data){
    exp(w_pH(beta,data[["prob.1"]])*data[["upper.1"]] + w_pL(beta,data[["prob.1"]])*data[["lower.1"]]) +
    exp(w_pH(beta,data[["prob.2"]])*data[["upper.2"]] + w_pL(beta,data[["prob.2"]])*data[["lower.2"]]) +
    exp(w_pH(beta,data[["prob.3"]])*data[["upper.3"]] + w_pL(beta,data[["prob.3"]])*data[["lower.3"]]) +
    exp(w_pH(beta,data[["prob.4"]])*data[["upper.4"]] + w_pL(beta,data[["prob.4"]])*data[["lower.4"]]) +
    exp(w_pH(beta,data[["prob.5"]])*data[["upper.5"]] + w_pL(beta,data[["prob.5"]])*data[["lower.5"]])
  }
  
  
  
  denomRes = apply(data, 1, denomCalc) #vector of denominator components for each student
  
  # calculate numerator of likelihood of a choice
  numerCalc = function(data){
    j = data[["choice"]]
    numercalc = exp(w_pH(beta,data[[13+j]])*data[[8+j]] + w_pL(beta,data[[13+j]])*data[[3+j]])
    numercalc
  }
  
  numerRes = apply(data, 1, numerCalc)
  
  #calculating log likelihood
  log_lik_i <-  log(numerRes/denomRes)
  
  -sum(unlist(log_lik_i))
}



sample_SR = function(data,sub_sample){
  if(sub_sample == "full"){data = data}
  if(sub_sample == "part1"){data = data %>% filter(qnum<19)}
  if(sub_sample == "part2"){data = data %>%  filter(qnum>18)}
  return(data)
}






